ME 6443 Variational Methods in Engineering

ME 6443: Variational Methods in Engineering
Offered Every Fall

Credit Hours:	3-0-3
Prerequisite:	Graduate standing in engineering or related discipline
Catalog Description:	Calculus of variations, Hamilton's principle and Lagrange's equations, Sturm-Liouville problems, approximation techniques.
Textbooks:	Robert Weinstock, Calculus of Variations, Dover Publications, 1980. Francis Hilderbrand, Methods of Applied Mathematics, 2nd Edition, Dover, 1992.
Instructors:	Aldo Ferri, Jerry Ginsberg (Fall 2004), John Papastavridis (Fall 2003)

Topics:

Introduction, review of min/max of functions, algebraic equality and inequality constraints; Lagrange multipliers
Basics of the calculus of variations
Isoperimetric constraints; finite and differential constraints
Hamilton's principle and Lagrange's equations
Sturm-Liouville problems
Functions of two variables or more variables; vibration of strings, rods, beams; static and dynamic deformation of membranes and plates
Approximation techniques; Ritz methods such as the Bubnov-Galerkin and Petrov-Galerkin techniques; method of weighted residuals; finite-element analysis
Optimal control theory; quadratic cost functions; two-point boundary-value problems; Riccati equation; optimal state-feedback.

Grading:

Homework 10%, Midterm 40%, Final Exam 50%

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Revised June 2004